Problem: Solve for $x$ and $y$ using substitution. ${-5x-y = -8}$ ${x = -2y+7}$
Explanation: Since $x$ has already been solved for, substitute $-2y+7$ for $x$ in the first equation. ${-5}{(-2y+7)}{- y = -8}$ Simplify and solve for $y$ $10y-35 - y = -8$ $9y-35 = -8$ $9y-35{+35} = -8{+35}$ $9y = 27$ $\dfrac{9y}{{9}} = \dfrac{27}{{9}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {x = -2y+7}\thinspace$ to find $x$ ${x = -2}{(3)}{ + 7}$ $x = -6 + 7$ ${x = 1}$ You can also plug ${y = 3}$ into $\thinspace {-5x-y = -8}\thinspace$ and get the same answer for $x$ : ${-5x - }{(3)}{= -8}$ ${x = 1}$